JEE Main 18 March 2021 Shift 1 Solved Paper

The radioactive sample disintegrates via two independent decays as shown in the figure,Here, λ is the net disintegrate constant.
λ1 is the first decay constant,
and λ2 is the second decay constant.
From the above figure,
λ=λ1+λ2...(i)
As, we know that,
Half-life, T1/2=‌

ln(2)

λ

⇒λ=‌

ln(2)

T1/2

Substituting in Eq. (i), we get
‌

ln(2)

T1/2

=‌

ln(2)

T1/2(01)

+‌

ln(2)

T1/2(2)

⇒T1/2=

T1/2(1)T1/2(2)

T1/2(1)+T1/2(2)